12. A wire of given material having length ℓ and area of cross section A has a resistance 10 Ω. What would be the resistance of another wire of the same material having length ℓ/4 and area of cross-section 2.5 A
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Answer: 1 Ω
Explanation: R₁= 10Ω having length ℓ₁ and area A₁
∴ R₁= ρℓ₁/A₁= 10Ω
if length is divided by 4 (i.e. ℓ₁/4) and area is made 2.5 A₁
∴ R₂= ρℓ₂/A₂
∴ R₂= ρℓ₁/4
2.5 A₁
∴ R₂= ρℓ₁/10A₁
∴ R₂= R₁/10
∴ R₂= 10/10 = 1Ω
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